How can one evaluate the indefinite integral $$\int \frac{\sqrt{x}+ 1}{\sqrt{x}-1} \,dx$$
First I tried to multiply by $\frac{\sqrt{x}+1}{\sqrt{x}+1}$, but I couldn't get the final result. I also tried to seperate the integral into two $$\int \frac{\sqrt{x}}{\sqrt{x}-1} dx + \int \frac{1}{\sqrt{x}-1} dx$$
which failed to lead to a solution either. Is there another method that can be used?